Trapezoids
LearningObjectives
- Understandand provethat the baseanglesof isoscelestrapezoidsare congruent.
- Understandand provethat if baseanglesin a trapezoidare congruent,it is an isoscelestrapezoid.
- Understandand provethat the diagonalsin an isoscelestrapezoidare congruent.
- Understandand provethat if the diagonalsin a trapezoidare congruent,the trapezoidis isosceles.
- Identifythe medianof a trapezoidand use its properties.
Introduction
Trapezoidsare particularlyuniquefiguresamongquadrilaterals.Theyhaveexactlyone pair of parallelsides
so unlikerhombi,squares,and rectangles,they arenotparallelograms.Thereare specialrelationshipsin
trapezoids,particularlyin isoscelestrapezoids.Rememberthat isoscelestrapezoidshavenon-parallelsides
that are of the samelengths.Theyalso havesymmetryalonga line that passesperpendicularlythrough
both bases.
IsoscelesTrapezoid
Non-isoscelesTrapezoid
BaseAnglesin IsoscelesTrapezoids
Previously, you learnedaboutthe BaseAnglesTheorem.The theoremstatesthat in an isoscelestriangle,
the two baseangles(oppositethe congruentsides)are congruent.The samepropertyholdstrue for
isoscelestrapezoids.The two anglesalongthe samebasein an isoscelestrianglewill also be congruent.
Thus,this createstwo pairsof congruentangles—onepair alongeachbase.
Theorem:The baseanglesof an isoscelestrapezoidare congruentExample 1
Examinetrapezoid